There are three different kinds of displacement: Inertial displacement,
according to the first law of physics; forced displacement according to
the second law, and resultant displacement; which is the resultant sum
of inertial and forced displacement. AFAIK there is no specific
differentiating symbol to distinguish one kind from another. The
symbols l, s, and d are used by various texts, more or less
indiscrimatly to signify displacements of any kind, regardless of how
they are caused.
I've made an effort to diffentiate them with l for inertial
displacement; s for forced displacement, and d for their sum; so that l
+ s = d, and since motion is a unit of displacement per a unit of time
t: l/t + s/t = d/t.
The first law of physics describes inertial displacement - a distance
(l) - of a body moving relatively through empty space when there is
nothing interacting with it so that it can travel at a constant speed
in a straight line.
The second law of physics describes forced displacement - a distance
(s) - from where it would have been, gone, or stayed, if not for being
forced to change its velocity by a force of contact - friction etc. -
with other bodies; so that the resultant motion d/t is what actually
Inertia [Only registered users see links. ]
The resistance to change in state of motion which all matter exhibits.
It's a concept, Shead, not a number with units, not a ratio.
Newton's First Law [Only registered users see links. ]
Also called the "law of inertia," Newton's first law states that a
body at rest remains at rest and a body in motion continues to move
at a constant velocity unless acted upon by an external force.
Newton's Second Law is about "inertial mass" [Only registered users see links. ]
A force F acting on a body gives it an acceleration a which is in
the direction of the force and has magnitude inversely proportional
to the mass m of the body: F = ma
Inertia is an intrinsic property of mass. Most of what follows is
quoted from [Only registered users see links. ]
Gravitational Mass F = GmM/r^2
Inertial Mass F = ma
Acceleration a = dv/dt
1) Inertial mass. This is mainly defined by Newton's law,
the all-too-famous F = ma, which states that when a force
F is applied to an object, it will accelerate
proportionally, and that constant of proportion is the
mass of that object. In very concrete terms, to determine
the inertial mass, you apply a force of F Newtons to an
object, measure the acceleration in m/s^2, and F/a will
give you the inertial mass m in kilograms.
2) Gravitational mass. This is defined by the force of
gravitation, which states that there is a gravitational
force between any pair of objects, which is given by
F = G m1 m2/r^2
where G is the universal gravitational constant, m1 and m2
are the masses of the two objects, and r is the distance
between them. This, in effect defines the gravitational
mass of an object.
As it turns out, these two masses are equal to each other
as far as we can measure. Also, the equivalence of these
two masses is why all objects fall at the same rate on
The only difference that we can find between inertial and
gravitational mass that we can find is the method.
Gravitational mass is measured by comparing the force of
gravity of an unknown mass to the force of gravity of a
known mass. This is typically done with some sort of
balance scale. The beauty of this method is that no matter
where, or what planet, you are, the masses will always
balance out because the gravitational acceleration on each
object will be the same. This does break down near
supermassive objects such as black holes and neutron stars
due to the high gradient of the gravitational field around
Inertial mass is found by applying a known force to an
unknown mass, measuring the acceleration, and applying
Newton's Second Law, m = F/a. This gives as accurate a
value for mass as the accuracy of your measurements. When
the astronauts need to be weighed in outer space, they
actually find their inertial mass in a special chair.
The interesting thing is that, physically, no difference
has been found between gravitational and inertial mass.
Many experiments have been performed to check the values
and the experiments always agree to within the margin of
error for the experiment. Einstein used the fact that
gravitational and inertial mass were equal to begin his
Theory of General Relativity in which he postulated that
gravitational mass was the same as inertial mass and that
the acceleration of gravity is a result of a "valley" or
slope in the space-time continuum that masses "fell down"
much as pennies spiral around a hole in the common
donation toy at your favorite chain store.
Useful references for Shead [Only registered users see links. ] [Only registered users see links. ] [Only registered users see links. ] [Only registered users see links. ] [Only registered users see links. ] [Only registered users see links. ]
That is because they are not correct. Nor, apparently, do you know what
displacement means. I found this extract from Arons to be pertinent.
Sons, 1998, pg. and onwards:
Many presentations start in by ignoring the fact that the words "force"
and "mass," which in everyday speech, are heavily loaded metaphors, are
being taken out of everyday context and given very sophisticated
technical meaning, completely unfamiliar to the learner.... Students
have, in general, not been made self-conscious about, or sensitive to,
such semantic shifts, and they continue to endow the terms with the
diffuse metaphorical meanings previously absorbed or encountered. It is
helpful to make students explicitly conscious of the fact that the
words remain the same but that the meanings are sharply revised.
... Learners' difficulties in encompassing the law of inertia and the
concept of force stem in large measure from the wealth of common sense
preconceptions and experiential "rules" that most of us assimilate to
our view of the behavior of massive bodies before we are introduced to
Newtonian physics. Some of these views are Aristotelian (e.g., the
necessity of continued application of a push to keep a body moving, it
being very difficult to abandon thinking of rest as a condition
fundamentally different from that of motion, or to accept the view
that, rather than asking what keeps a body moving, we should ask what
causes it to stop), but many of these common sense views are more
closely related to the medieval notions of impetus associated with
names such as Buridan and Oresme.
All investigations show these "naive" conceptions to be very deeply
entrenched and very tenaciously held, and it is important for teachers
to understand that student difficulties are not reflections of
"stupidity" or recalcitrance. The difficulties are rooted in seemingly
logical consequences of perceived order and experience and are
vigorously reinforced by insistent use (or actually misuse) of words
drawn from everyday speech (inertia, mass, force, momentum, energy,
power, resistance) before these words have been given precise
operational meaning in physics. Persistent misuse of the terms in
thinking to oneself and in communicating with others is a major
obstacle to breaking away from the naive preconceptions.
... Investigations of understanding of the law of inertia further show
that it is far from sufficient to inculcate the law verbally and
supplement it with a few demonstrations of the behavior of frictionless
pucks on a table or gliders on an air track. Many students will
memorize and repeat the first law quite correctly in words but, when
confronted with the necessity of making predictions and describing what
happens in actual physical situations, concretely accessible to them,
they revert repeatedly to the naive preconceptions and predictions....
Quite a spiel PD, but I fail to see the pertinence. Students should be
taught to think and question things for themselves; including the
relativity of displacements: Where bodies continually change their
positions due to their inertial (relative) motion, and forced (changes
in) inertial motion.
It's very pertinent. It cautions students to not try to conflate
common-use definitions for terms with the precise meanings that are
developed as used in physics. The only way to *not* adopt those
meanings and avoid running into contradictions and unsound results is
to carefully and systematically *redefine* those terms, being careful
to advise the audience that you're doing so.
For example, in the above, what you call "relativity of displacements"
and "inertial (relative) motion" do not have any obvious bearing on
similar-sounding terms as they are used in physics. That means either
you do not understand the terms as they are used in physics, or you are
using the same words but attach different meanings which you have not
Agreed. It cautions teachers to warn students about that conflation.
That's why it's not done very often. Every once in a while, though, it
is required, and there are masters at it. Einstein did it. Feynman did
it. But they also had mastery of the previous meanings of those words.
Herman Trivilino wrote:
I agree with those meanings Herman; but at the same time, I also think
of _rates_ of acceleration, and rates of free fall: They express the
value of longivity of acceleration and free fall. Like the rate of free
fall found by Galileo; where g/2 = (about) 16' per second, per second.